An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.(1 point)

Question

Responses

180−20x=140−16x ; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20

180−20x=140−16x ; x=10
180 minus 20 x equals 140 minus 16 x ; x equals 10

140+16x=180+20x ; x=10
140 plus 16 x equals 180 plus 20 x ; x equals 10

180+16x=140+20x ; x=−10

Answer 1

Let's formulate the equations and solve for \( x \), where \( x \) represents the number of days.

1. The amount of vanilla ice cream left after \( x \) days can be represented as: \[ 180 - 20x \] This accounts for the initial capacity of 180 cups, minus 20 cups sold per day.

2. The amount of chocolate ice cream left after \( x \) days can be represented as: \[ 140 - 16x \] This accounts for the initial capacity of 140 cups, minus 16 cups sold per day.

We want to find the day \( x \) when the amounts of ice cream left in both machines are equal: \[ 180 - 20x = 140 - 16x \]

Now, let's solve this equation step by step:

1. Start by moving all terms involving \( x \) to one side and constant terms to the other side: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \]

2. Divide both sides by 4: \[ x = 10 \]

Thus, the correct response is: \[ 180 - 20x = 140 - 16x; \quad x = 10 \]

This corresponds to the second response option.

In summary: 180 − 20x = 140 − 16x; x = 10